# doubt on iid distribution vs uniform distribution

I am a bit confused when I read "iid distribution".

It looks to me like what is called "uniform distribution" i.e. a distribution of probability that is constant in a range. Am I correct in thinking this?

What distributions could be considered "iid" other than the simple "uniform" one? Reading on Wikipedia it is mentioned Levy Processes, not even the uniform. In which way should I think of what is supposed to be an IID distribution?

Kind Regards AFG

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There is absolutely no connection with uniform distribution. A bunch of IID random variables might have the same uniform distribution, but they might have the same normal distribution, or Poisson distribution. –  André Nicolas Oct 3 '11 at 20:12
At the risk of repeating things already said: iid distribution means nothing. The phrase is iid random variables (random variables instead of distribution, and plural instead of singular). –  Did Oct 4 '11 at 7:10
Hi Didier. You are right. Reading back the question I think is not very well posted..let's say that it reveals doubt I had before all these responses. –  Abruzzo Forte e Gentile Oct 4 '11 at 8:21

## 1 Answer

It means "independent and identically distributed", it is used referring to some random variables, to say they are independent from each other and have the same distribution.

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Ah! Just simple like that! Maybe I am not focused at the moment, but it looked to me really complicated stuff. So basically "indipendent" is the only requirement for them + all coming from the same distribution WHATEVER it is. Thanks a lot! –  Abruzzo Forte e Gentile Oct 3 '11 at 20:28
Indeed it is simple. The idea comes up often, because we are often interested in what happens when we repeat an experiment (like tossing a pair of dice) several times. –  André Nicolas Oct 3 '11 at 20:55